Investigating Custodial Symmetry Violation in the Georgi-Machacek

The Georgi-Machacek (GM) model is the simplest benchmark model for higher isospin multiplet extensions of the Standard Model (SM) which allow for large contributions to electro-weak symmetry breaking (EWSB) from these 'exotic' multiplets.It is used to motivate and interpret Large Hadron Collider (LHC) searches for doubly charged scalars decaying to vector boson pairs.It preserves custodial symmetry (CS) at tree level; however, this CS has long been known to be violated at the one-loop level by hypercharge interactions.In this thesis, we study the effects of CS violation (CV).We assume that the CS GM model arises at a high scale as a result of an unspecified ultraviolet (UV) completion, and quantify the CV induced at the weak scale.We show that experimental data constrains the UV scale to lie below tens to hundreds of TeV over almost all of the parameter space.Subject to this constraint, we quantify the size of other CV effects at the weak scale and we find that these effects are small enough that they are unlikely to be probed by the LHC, but may be detectable at a future e + e -collider.We note that the upper bound on the UV scale is large enough that virtual effects from the UV completion will likely be undetectable at the LHC.This means that the GM model is a valid effective theory for LHC physics.We also propose a new "low-m 5 " benchmark for the tree level GM model, defined for m 5 ∈ (50, 550) GeV, and characterize its properties.This benchmark plane is designed to facilitate the extension of current collider searches for doubly charged scalars to an unexplored region of parameter space which was not previously covered by a benchmark plane.The doubly charged scalars are part of a degenerate fermiophobic custodial fiveplet with states H ±± 5 , H ± 5 , and H 0 5 and the input parameter m 5 is their common mass.We apply all existing experimental constraints and summarize the phenomenology of the surviving parameter space.We show that there is a largely i unprobed region of parameter space from 120 GeV < m 5 < 200 GeV where light doubly-charged scalars could exist.to list all the friends, family, professors, students, teaching assistants, colleagues, and casual acquaintances who at various times have given me their time, their support, or served as a source of motivation or inspiration, I am afraid that I have always found words a poor medium for the adequate expression of gratitude and if I were to attempt to individually thank everyone who deserved it, I am sure that I would run on and on to little purpose.For all who have had a positive impact on this thesis, especially those not specifically mentioned below, I hope it will suffice to merely state that you have my most sincere thanks; at the very least as much thanks as you think you deserve and in some cases undoubtedly far more than you could ever know.With the above sentiment in mind, I will only specifically acknowledge the contributions of a select few of many deserving people.Firstly, I am extremely grateful to my supervisor Heather Logan who has made this process as enjoyable and rewarding as one could possibly hope.

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